Atkin-Lehner |
2- 5- 7- |
Signs for the Atkin-Lehner involutions |
Class |
78400ko |
Isogeny class |
Conductor |
78400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
153600 |
Modular degree for the optimal curve |
Δ |
-102942875000000 = -1 · 26 · 59 · 77 |
Discriminant |
Eigenvalues |
2- -1 5- 7- -3 1 -7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,8167,-399713] |
[a1,a2,a3,a4,a6] |
Generators |
[42:125:1] [306:5537:1] |
Generators of the group modulo torsion |
j |
4096/7 |
j-invariant |
L |
8.6074109262959 |
L(r)(E,1)/r! |
Ω |
0.31369020350456 |
Real period |
R |
3.4299010736271 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78400ej1 19600ds1 78400kj1 11200df1 |
Quadratic twists by: -4 8 5 -7 |